5 Search Results for "Yuditsky, Yelena"

Document
DOI: 10.4230/LIPIcs.SoCG.2022.33
A Solution to Ringel’s Circle Problem

Authors: James Davies, Chaya Keller, Linda Kleist, Shakhar Smorodinsky, and Bartosz Walczak

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
We construct families of circles in the plane such that their tangency graphs have arbitrarily large girth and chromatic number. This provides a strong negative answer to Ringel’s circle problem (1959). The proof relies on a (multidimensional) version of Gallai’s theorem with polynomial constraints, which we derive from the Hales-Jewett theorem and which may be of independent interest.
Cite as

James Davies, Chaya Keller, Linda Kleist, Shakhar Smorodinsky, and Bartosz Walczak. A Solution to Ringel’s Circle Problem. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 33:1-33:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{davies_et_al:LIPIcs.SoCG.2022.33,
  author =	{Davies, James and Keller, Chaya and Kleist, Linda and Smorodinsky, Shakhar and Walczak, Bartosz},
  title =	{{A Solution to Ringel’s Circle Problem}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{33:1--33:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.33},
  URN =		{urn:nbn:de:0030-drops-160413},
  doi =		{10.4230/LIPIcs.SoCG.2022.33},
  annote =	{Keywords: circle arrangement, chromatic number, Gallai’s theorem, polynomial method}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2022.38
On Comparable Box Dimension

Authors: Zdeněk Dvořák, Daniel Gonçalves, Abhiruk Lahiri, Jane Tan, and Torsten Ueckerdt

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
Two boxes in ℝ^d are comparable if one of them is a subset of a translation of the other one. The comparable box dimension of a graph G is the minimum integer d such that G can be represented as a touching graph of comparable axis-aligned boxes in ℝ^d. We show that proper minor-closed classes have bounded comparable box dimension and explore further properties of this notion.
Cite as

Zdeněk Dvořák, Daniel Gonçalves, Abhiruk Lahiri, Jane Tan, and Torsten Ueckerdt. On Comparable Box Dimension. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 38:1-38:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dvorak_et_al:LIPIcs.SoCG.2022.38,
  author =	{Dvo\v{r}\'{a}k, Zden\v{e}k and Gon\c{c}alves, Daniel and Lahiri, Abhiruk and Tan, Jane and Ueckerdt, Torsten},
  title =	{{On Comparable Box Dimension}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{38:1--38:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.38},
  URN =		{urn:nbn:de:0030-drops-160461},
  doi =		{10.4230/LIPIcs.SoCG.2022.38},
  annote =	{Keywords: geometric graphs, minor-closed graph classes, treewidth fragility}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2022.39
Weak Coloring Numbers of Intersection Graphs

Authors: Zdeněk Dvořák, Jakub Pekárek, Torsten Ueckerdt, and Yelena Yuditsky

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
Weak and strong coloring numbers are generalizations of the degeneracy of a graph, where for a positive integer k, we seek a vertex ordering such that every vertex can (weakly respectively strongly) reach in k steps only few vertices that precede it in the ordering. Both notions capture the sparsity of a graph or a graph class, and have interesting applications in structural and algorithmic graph theory. Recently, Dvořák, McCarty, and Norin observed a natural volume-based upper bound for the strong coloring numbers of intersection graphs of well-behaved objects in ℝ^d, such as homothets of a compact convex object, or comparable axis-aligned boxes. In this paper, we prove upper and lower bounds for the k-th weak coloring numbers of these classes of intersection graphs. As a consequence, we describe a natural graph class whose strong coloring numbers are polynomial in k, but the weak coloring numbers are exponential. We also observe a surprising difference in terms of the dependence of the weak coloring numbers on the dimension between touching graphs of balls (single-exponential) and hypercubes (double-exponential).
Cite as

Zdeněk Dvořák, Jakub Pekárek, Torsten Ueckerdt, and Yelena Yuditsky. Weak Coloring Numbers of Intersection Graphs. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 39:1-39:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dvorak_et_al:LIPIcs.SoCG.2022.39,
  author =	{Dvo\v{r}\'{a}k, Zden\v{e}k and Pek\'{a}rek, Jakub and Ueckerdt, Torsten and Yuditsky, Yelena},
  title =	{{Weak Coloring Numbers of Intersection Graphs}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{39:1--39:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.39},
  URN =		{urn:nbn:de:0030-drops-160477},
  doi =		{10.4230/LIPIcs.SoCG.2022.39},
  annote =	{Keywords: geometric intersection graphs, weak and strong coloring numbers}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2020.5
The ε-t-Net Problem

Authors: Noga Alon, Bruno Jartoux, Chaya Keller, Shakhar Smorodinsky, and Yelena Yuditsky

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
We study a natural generalization of the classical ε-net problem (Haussler - Welzl 1987), which we call the ε-t-net problem: Given a hypergraph on n vertices and parameters t and ε ≥ t/n, find a minimum-sized family S of t-element subsets of vertices such that each hyperedge of size at least ε n contains a set in S. When t=1, this corresponds to the ε-net problem. We prove that any sufficiently large hypergraph with VC-dimension d admits an ε-t-net of size O((1+log t)d/ε log 1/ε). For some families of geometrically-defined hypergraphs (such as the dual hypergraph of regions with linear union complexity), we prove the existence of O(1/ε)-sized ε-t-nets. We also present an explicit construction of ε-t-nets (including ε-nets) for hypergraphs with bounded VC-dimension. In comparison to previous constructions for the special case of ε-nets (i.e., for t=1), it does not rely on advanced derandomization techniques. To this end we introduce a variant of the notion of VC-dimension which is of independent interest.
Cite as

Noga Alon, Bruno Jartoux, Chaya Keller, Shakhar Smorodinsky, and Yelena Yuditsky. The ε-t-Net Problem. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{alon_et_al:LIPIcs.SoCG.2020.5,
  author =	{Alon, Noga and Jartoux, Bruno and Keller, Chaya and Smorodinsky, Shakhar and Yuditsky, Yelena},
  title =	{{The \epsilon-t-Net Problem}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{5:1--5:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.5},
  URN =		{urn:nbn:de:0030-drops-121639},
  doi =		{10.4230/LIPIcs.SoCG.2020.5},
  annote =	{Keywords: epsilon-nets, geometric hypergraphs, VC-dimension, linear union complexity}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2018.68
Almost All String Graphs are Intersection Graphs of Plane Convex Sets

Authors: János Pach, Bruce Reed, and Yelena Yuditsky

Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)

Abstract
A string graph is the intersection graph of a family of continuous arcs in the plane. The intersection graph of a family of plane convex sets is a string graph, but not all string graphs can be obtained in this way. We prove the following structure theorem conjectured by Janson and Uzzell: The vertex set of almost all string graphs on n vertices can be partitioned into five cliques such that some pair of them is not connected by any edge (n --> infty). We also show that every graph with the above property is an intersection graph of plane convex sets. As a corollary, we obtain that almost all string graphs on n vertices are intersection graphs of plane convex sets.
Cite as

János Pach, Bruce Reed, and Yelena Yuditsky. Almost All String Graphs are Intersection Graphs of Plane Convex Sets. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 68:1-68:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{pach_et_al:LIPIcs.SoCG.2018.68,
  author =	{Pach, J\'{a}nos and Reed, Bruce and Yuditsky, Yelena},
  title =	{{Almost All String Graphs are Intersection Graphs of Plane Convex Sets}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{68:1--68:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Speckmann, Bettina and T\'{o}th, Csaba D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.68},
  URN =		{urn:nbn:de:0030-drops-87818},
  doi =		{10.4230/LIPIcs.SoCG.2018.68},
  annote =	{Keywords: String graph, intersection graph, plane convex set}
}
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